Abstract Over the past decade, microfacet‐based BRDF models have formed the foundation of real‐time rendering pipelines. Despite their widespread use, they often fail to reproduce subtle appearance effects arising from complex light–surface interactions, which have led to the emergence of specialized physics‐based models for specific optical phenomena (e.g., diffraction, iridescence, multilayers). Although more accurate, these models lose versatility and lack performance for real‐time rendering. Recently introduced, neural models have demonstrated their ability to approximate BRDF reference data coming from measurements, simulations, or even complex shading networks. However, most current neural models require relatively large networks, making them costly for real‐time rendering. In this paper, we introduce a hybrid model that combines a GGX‐type microfacet model and a neural model to leverage the best features of both representations. The neural component corrects the appearance approximated by the microfacet component, allowing much smaller network than in existing neural models. We show that, at identical memory cost, our model approximates measurements better than state‐of‐the‐art neural models for a low evaluation overhead compared to a microfacet‐based model. Furthermore, our hybrid model remains easily editable by artists and benefits from an important sampling scheme, making it attractive for both offline and real‐time rendering.

Abstract Importance sampling of visible normal distribution functions (vNDF) is a required ingredient for the efficient rendering of microfacet‐based materials. In this paper, we explain how to sample the vNDF for the micrograin material model [LRPB23], which has been recently improved to handle height‐normal correlations through a new Geometric Attenuation Factor (GAF) [LRPB24], leading to a stronger impact on appearance compared to the earlier Smith approximation. To this end, we make two contributions: we derive analytic expressions for the marginal and conditional cumulative distribution functions (CDFs) of the vNDF; we provide efficient methods for inverting these CDFs based respectively on a 2D lookup table and on the triangle‐cut method [Hei20].

Abstract Many animals, plants or gems exhibit iridescent material appearance in nature. These are due to specific geometric structures at scales comparable to visible wavelengths, yielding so‐called structural colors. The most vivid examples are due to photonic crystals, where a same structure is repeated in one, two or three dimensions, augmenting the magnitude and complexity of interference effects. In this paper, we study the appearance of 1D photonic crystals (repetitive pairs of thin films), also called Bragg mirrors. Previous work has considered the effect of multiple thin films using the classical transfer matrix approach, which increases in complexity when the number of repetitions increases. Our first contribution is to introduce a more efficient closed‐form reflectance formula [Yeh88] for Bragg mirror reflectance to the Graphics community, as well as an approximation that lends itself to efficient spectral integration for RGB rendering. We then explore the appearance of stacks made of rough Bragg layers. Here our contribution is to show that they may lead to a ballistic transmission, significantly speeding up position‐free rendering and leading to an efficient single‐reflection BRDF model.

We introduce an improved version of the micrograin BSDF model [Lucas et al. 2023] for the rendering of anisotropic porous layers. Our approach leverages the properties of micrograins to take into account the correlation between their height and normal, as well as the correlation between the light and view directions. This allows us to derive an exact analytical expression for the Geometrical Attenuation Factor (GAF), summarizing shadowing and masking inside the porous layer. This fully-correlated GAF is then used to define appropriate mixing weights to blend the BSDFs of the porous and base layers. Furthermore, by generalizing the micrograins shape to anisotropy, combined with their fully-correlated GAF, our improved BSDF model produces effects specific to porous layers such as retro-reflection visible on dust layers at grazing angles or height and color correlation that can be found on rusty materials. Finally, we demonstrate very close matches between our BSDF model and light transport simulations realized with explicit instances of micrograins, thus validating our model.

We introduce a new BSDF model for the rendering of porous layers, as found on surfaces covered by dust, rust, dirt, or sprayed paint. Our approach is based on a distribution of elliptical opaque micrograins, extending the Trowbridge-Reitz (GGX) distribution [Trowbridge and Reitz 1975; Walter et al. 2007] to handle pores (i.e., spaces between micrograins). We use distance field statistics to derive the corresponding Normal Distribution Function (NDF) and Geometric Attenuation Factor (GAF), as well as a view- and light-dependent filling factor to blend between the porous and base layers. All the derived terms show excellent agreement when compared against numerical simulations.

Layered materials exhibit a wide range of appearance, due to the combined effects of absorption and scattering at and between interfaces. Yet most existing approaches let users set the physical parameters of all layers by hand, a process of trial and error. We introduce an inverse method that provides control over BRDF lobe properties of layered materials, while automatically retrieving compatible physical parameters. Our method permits to explore the space of layered material appearance: it lets users find configurations with nearly indistinguishable appearance, isolate grazing angle effects, and give control over properties such as the color, blur or haze of reflections.

Abstract We introduce a bidirectional reflectance distribution function (BRDF) model for the rendering of materials that exhibit hazy reflections, whereby the specular reflections appear to be flanked by a surrounding halo. The focus of this work is on artistic control and ease of implementation for real‐time and off‐line rendering. We propose relying on a composite material based on a pair of arbitrary BRDF models; however, instead of controlling their physical parameters, we expose perceptual parameters inspired by visual experiments [ VBF17 ]. Our main contribution then consists in a mapping from perceptual to physical parameters that ensures the resulting composite BRDF is valid in terms of reciprocity, positivity and energy conservation. The immediate benefit of our approach is to provide direct artistic control over both the intensity and extent of the haze effect, which is not only necessary for editing purposes, but also essential to vary haziness spatially over an object surface. Our solution is also simple to implement as it requires no new importance sampling strategy and relies on existing BRDF models. Such a simplicity is key to approximating the method for the editing of hazy gloss in real‐time and for compositing.

Adequate reflectance models are essential for the production of photorealistic images. Microfacet reflectance models predict the appearance of a material at the macroscopic level based on microscopic surface details. They provide a good match with measured reflectance in some cases, but not always. This discrepancy between the behavior predicted by microfacet models and the observed behavior has puzzled researchers for a long time. In this paper, we show that diffraction effects in the micro-geometry provide a plausible explanation. We describe a two-scale reflectance model, separating between geometry details much larger than wavelength and those of size comparable to wavelength. The former model results in the standard Cook-Torrance model. The latter model is responsible for diffraction effects. Diffraction effects at the smaller scale are convolved by the micro-geometry normal distribution. The resulting two-scale model provides a very good approximation to measured reflectances.

The possibility to use real world light sources (aka luminaires) for synthesizing images greatly contributes to their physical realism. Among existing models, the ones based on light fields are attractive due to their ability to represent faithfully the near-field and due to their possibility of being directly acquired. In this paper, we introduce a dynamic sampling strategy for complex light field luminaires with the corresponding unbiased estimator. The sampling strategy is adapted, for each 3D scene position and each frame, by restricting the sampling domain dynamically and by balancing the number of samples between the different components of the representation. This is achieved efficiently by simple position-dependent affine transformations and restrictions of Cumulative Distributive Functions that ensure that every generated sample conveys energy and contributes to the final result. Therefore, our approach only requires a low number of samples to achieve almost converged results. We demonstrate the efficiency of our approach on modern hardware by introducing a GPU-based implementation. Combined with a fast shadow algorithm, our solution exhibits interactive frame rates for direct lighting for large measured luminaires.

Abstract This paper introduces a system for the direct editing of highlights produced by anisotropic BRDFs, which we call anisotropic highlights. We first provide a comprehensive analysis of the link between the direction of anisotropy and the shape of highlight curves for arbitrary object surfaces. The gained insights provide the required ingredients to infer BRDF orientations from a prescribed highlight tangent field. This amounts to a non‐linear optimization problem, which is solved at interactive framerates during manipulation. Taking inspiration from sculpting software, we provide tools that give the impression of manipulating highlight curves while actually modifying their tangents. Our solver produces desired highlight shapes for a host of lighting environments and anisotropic BRDFs.

Abstract Monte Carlo Techniques are widely used in Computer Graphics to generate realistic images. Multiple Importance Sampling reduces the impact of choosing a dedicated strategy by balancing the number of samples between different strategies. However, an automatic choice of the optimal balancing remains a difficult problem. Without any scene characteristics knowledge, the default choice is to select the same number of samples from different strategies and to use them with heuristic techniques (e.g., balance, power or maximum). In this paper, we introduce a second‐order approximation of variance for balance heuristic. Based on this approximation, we introduce an automatic distribution of samples for direct lighting without any prior knowledge of the scene characteristics. We demonstrate that for all our test scenes (with different types of materials, light sources and visibility complexity), our method actually reduces variance in average. We also propose an implementation with low overhead for offline and GPU applications. We hope that this approach will help developing new balancing strategies.

Over the last two decades, much effort has been devoted to accurately measuring Bidirectional Reflectance Distribution Functions (BRDFs) of real-world materials and to use efficiently the resulting data for rendering. Because of their large size, it is difficult to use directly measured BRDFs for real-time applications, and fitting the most sophisticated analytical BRDF models is still a complex task. In this paper, we introduce Rational BRDF, a general-purpose and efficient representation for arbitrary BRDFs, based on Rational Functions (RFs). Using an adapted parametrization, we demonstrate how Rational BRDFs offer 1) a more compact and efficient representation using low-degree RFs, 2) an accurate fitting of measured materials with guaranteed control of the residual error, and 3) efficient importance sampling by applying the same fitting process to determine the inverse of the Cumulative Distribution Function (CDF) generated from the BRDF for use in Monte-Carlo rendering.

Based on the observation that shading conveys shape information through intensity gradients, we present a new technique called Radiance Scaling that modifies the classical shading equations to offer versatile shape depiction functionalities. It works by scaling reflected light intensities depending on both surface curvature and material characteristics. As a result, diffuse shading or highlight variations become correlated with surface feature variations, enhancing concavities and convexities. The first advantage of such an approach is that it produces satisfying results with any kind of material for direct and global illumination: we demonstrate results obtained with Phong and Ashikmin-Shirley BRDFs, Cartoon shading, sub-Lambertian materials, perfectly reflective or refractive objects. Another advantage is that there is no restriction to the choice of lighting environment: it works with a single light, area lights, and interreflections. Third, it may be adapted to enhance surface shape through the use of precomputed radiance data such as Ambient Occlusion, Prefiltered Environment Maps or Lit Spheres. Finally, our approach works in real time on modern graphics hardware making it suitable for any interactive 3D visualization.

We present a novel technique called Radiance Scaling for the depiction of surface shape through shading. It adjusts reflected light intensities in a way dependent on both surface curvature and material characteristics. As a result, diffuse shading or highlight variations become correlated to surface feature variations, enhancing surface concavities and convexities. This approach is more versatile compared to previous methods. First, it produces satisfying results with any kind of material: we demonstrate results obtained with Phong and Ashikmin BRDFs, Cartoon shading, sub-Lambertian materials, and perfectly reflective or refractive objects. Second, it imposes no restriction on lighting environment: it does not require a dense sampling of lighting directions and works even with a single light. Third, it makes it possible to enhance surface shape through the use of precomputed radiance data such as Ambient Occlusion, Prefiltered Environment Maps or Lit Spheres. Our novel approach works in real-time on modern graphics hardware.

Recent research on the human visual system shows that our perception of object shape relies in part on compression and stretching of the reflected lighting environment onto its surface. We use this property to enhance the shape depiction of 3D objects by locally warping the environment lighting around main surface features. Contrary to previous work, which require specific illumination, material characteristics and/or stylization choices, our approach enhances surface shape without impairing the desired appearance. Thanks to our novel local shape descriptor, salient surface features are explicitly extracted in a view-dependent fashion at various scales without the need of any pre-process. We demonstrate our system on a variety of rendering settings, using object materials ranging from diffuse to glossy, to mirror or refractive, with direct or global illumination, and providing styles that range from photorealistic to non-photorealistic. The warping itself is very fast to compute on modern graphics hardware, enabling real-time performance in direct illumination scenarios. Note: Third-Party Material Attribution Third-party material used in ACM Transactions on Graphics 28(3), Article 25 - "Light Warping for Enhanced Surface Depiction," by Vergne, Pacanowski, Barla, Granier, and Schlick - was used without proper attribution. The 3D model used in Figures 1, 3, and 5, as well as in the cover image of this volume of the journal, was downloaded from the Shape Repository of AIM@SHAPE Project (http://shapes.aimatshape.net) and is the property of CNR-IMATI. We regret this oversight.